Kinematic Dependence Research Articles

Sivers asymmetry extracted in SIDIS at the hard scales of the Drell–Yan process at COMPASS

Eight proton transverse-spin-dependent azimuthal asymmetries are extracted in four regions of the photon virtuality Q2 from the COMPASS 2010 semi-inclusive hadron measurements in deep inelastic muon–nucleon scattering. These Q2 regions correspond to the four regions of the di-muon mass Q2 used in the ongoing analyses of the COMPASS Drell–Yan measurements, which allows for a future direct comparison of the nucleon transverse-momentum-dependent parton distribution functions extracted from these two alternative measurements. In addition, for the azimuthal asymmetries induced by the Sivers transverse-momentum-dependent parton distribution function various two-dimensional kinematic dependences are presented. The integrated Sivers asymmetries are found to be positive with an accuracy that appears to be sufficient to test the sign change of the Sivers function predicted by Quantum Chromodynamics.

Light-by-Light Hadronic Corrections to the Muon G-2 Problem Within the Nonlocal Chiral Quark Model

Results of calculation of the light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons and the dynamical quark loop to the muon anomalous magnetic moment are discussed in the framework of the nonlocal SU(3) × SU(3) chiral quark model. The model is based on four-quark interaction of the Nambu–Jona–Lasinio type and Kobayashi–Maskawa–‘t Hooft six-quark interaction. The full kinematic dependence of vertices with off-shell mesons and photons in intermediate states in the light-by-light scattering amplitude is taken into account. All calculations are elaborated in explicitly gauge-invariant manner. These results complete calculations of all hadronic light-by-light scattering contributions to aμ in the leading order in the 1/Nc expansion. The final result does not allow the discrepancy between the experiment and the Standard Model to be explained.

Specific Features of Friction-Type Traction Gear of Rotating Machines Drives

The paper reviews specific operational features of the friction-type traction gear typically used in track-guided vehicles when applied to the drives of rotating machines. A design of the friction-type traction gear that uses a circular rail is presented. The provided layout drawing shows the position of the traction gear wheels against the circular rail as well as the pattern of forces acting on the traction gear. Basic geometrical, kinematic, and force dependences are established for the traction gear mounted on a circular rail. Based on the performed analysis, the recommendations regarding the use of friction-type traction gears as drives for the rotating machines are provided.

Mechanism of a Motion Platform Inducing the Movement of the Operator’s Seat in a Heavy Machine

One of the major work safety issues involves the investigations of machine vibrations and the way they affect the machine operators. These investigations can be performed in the laboratory conditions in a setup in which the seat vibrations are induced by a motion platform. A complex mechanism is proposed implementing 3 translations and 2 rotation movements, and actuated by three electric motors. This study investigates the design structure of the real motion platform mechanism and provides the synthesis of link dimensioning. Kinematic dependencies are formulated and the Jacobian matrix is derived accordingly to solve the equations of motion. Computer simulation procedure yields the critical seat vibration frequency and amplitudes for the available asynchronous motors.

Three-Loop Corrections to the Soft Anomalous Dimension in Multileg Scattering.

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multileg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that nondipole corrections appear already for three colored partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally invariant cross ratios for four colored partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the nondipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it depends only on the color charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally, we verify that our result is consistent with expectations from the Regge limit.

All orders results for self-crossing Wilson loops mimicking double parton scattering

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. We also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

A novel look at energy equipartition in globular clusters

Two-body interactions play a major role in shaping the structural and dynamical properties of globular clusters (GCs) over their long-term evolution. In particular, GCs evolve toward a state of partial energy equipartition that induces a mass-dependence in their kinematics. By using a set of Monte Carlo cluster simulations evolved in quasi-isolation, we show that the stellar mass dependence of the velocity dispersion $\sigma(m)$ can be described by an exponential function $\sigma^2\propto \exp(-m/m_\mathrm{eq})$, with the parameter $m_\mathrm{eq}$ quantifying the degree of partial energy equipartition of the systems. This simple parametrization successfully captures the behaviour of the velocity dispersion at lower as well as higher stellar masses, that is, the regime where the system is expected to approach full equipartition. We find a tight correlation between the degree of equipartition reached by a GC and its dynamical state, indicating that clusters that are more than about 20 core relaxation times old, have reached a maximum degree of equipartition. This equipartition$-$dynamical state relation can be used as a tool to characterize the relaxation condition of a cluster with a kinematic measure of the $m_\mathrm{eq}$ parameter. Vice versa, the mass-dependence of the kinematics can be predicted knowing the relaxation time solely on the basis of photometric measurements. Moreover, any deviations from this tight relation could be used as a probe of a peculiar dynamical history of a cluster. Finally, our novel approach is important for the interpretation of state-of-the-art Hubble Space Telescope proper motion data, for which the mass dependence of kinematics can now be measured, and for the application of modeling techniques which take into consideration multi-mass components and mass segregation.

Study of the Hyperon-Nucleon Interaction in Exclusive Λ Photoproduction off the Deuteron

The study of final-state interactions in exclusive hyperon photoproduction off the deuteron is a promising approach to extract information about the hyperon-nucleon (YN) interaction. First preliminary results on the azimuthal asymmetry ∑, as well as the polarization transfer coeffcients Ox, Oz, Cx, and Cz for the reaction γd → K+ Λn initiated with linearly and circularly polarized photon beam are presented. The data were taken with the CLAS detector in Hall B of Jefferson Lab during the E06-103 experiment. The large kinematic coverage of the CLAS, combined with the exceptionally high quality of the experimental data, allows identifying and selecting final-state interaction events to extract single- and double-polarization observables and their kinematical dependencies.

MAGiiCAT V. ORIENTATION OF OUTFLOWS AND ACCRETION DETERMINE THE KINEMATICS AND COLUMN DENSITIES OF THE CIRCUMGALACTIC MEDIUM

We investigate the dependence of gas kinematics and column densities in the MgII-absorbing circumgalactic medium on galaxy color, azimuthal angle, and inclination to trace baryon cycle processes. Our sample of 30 foreground isolated galaxies at $0.3<z_{\rm gal}<1.0$, imaged with the Hubble Space Telescope, are probed by background quasars within a projected distance of $20<D<110$ kpc. From the high-resolution ($\Delta v\simeq 6.6$ km s$^{-1}$) quasar spectra, we quantify the extent of the absorber velocity structure with pixel-velocity two-point correlation functions. Absorbers with the largest velocity dispersions are associated with blue, face-on ($i<57^{\circ}$) galaxies probed along the projected minor axis ($\Phi \geq 45^{\circ}$), while those with the smallest velocity dispersions belong to red, face-on galaxies along the minor axis. The velocity structure is similar for edge-on ($i \geq 57^{\circ}$) galaxies regardless of galaxy color or azimuthal angle, for red galaxies with azimuthal angle, and for blue and red galaxies probed along the projected major axis ($\Phi<45^{\circ}$). The cloud column densities for face-on galaxies and red galaxies are smaller than for edge-on galaxies and blue galaxies, respectively. These results are consistent with biconical outflows along the minor axis for star-forming galaxies and accreting and/or rotating gas, which is most easily observed in edge-on galaxies probed along the major axis. Gas entrained in outflows may be fragmented with large velocity dispersions, while gas accreting onto or rotating around galaxies may be more coherent due to large path lengths and smaller velocity dispersions. Quiescent galaxies may exhibit little-to-no outflows along the minor axis, while accretion/rotation may exist along the major axis.

Measurement of differentialJ/ψproduction cross sections and forward-backward ratios inp + Pbcollisions with the ATLAS detector

Measurements of differential cross-sections for $J/\psi$ production in p+Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV at the LHC with the ATLAS detector are presented. The data set used corresponds to an integrated luminosity of 28.1 nb$^{-1}$. The $J/\psi$ mesons are reconstructed in the dimuon decay channel over the transverse momentum range $8<p_{\mathrm{T}}<30$ GeV and over the center-of-mass rapidity range $-2.87<y^{*}<1.94$. Prompt $J/\psi$ are separated from $J/\psi$ resulting from $b$-hadron decays through an analysis of the distance between the $J/\psi$ decay vertex and the event primary vertex. The differential cross-section for production of nonprompt $J/\psi$ is compared to a FONLL calculation that does not include nuclear effects. Forward-backward production ratios are presented and compared to theoretical predictions. These results constrain the kinematic dependence of nuclear modifications of charmonium and $b$-quark production in p+Pb collisions.

Single and double spin asymmetries for deeply virtual Compton scattering measured with CLAS and a longitudinally polarized proton target

Single-beam, single-target, and double-spin asymmetries for hard exclusive photon production on the proton $\vec{e}\vec{p} \to e' p'\gamma$ are presented. The data were taken at Jefferson Lab using the CLAS detector and a longitudinally polarized ${}^{14}$NH$_3$ target. The three asymmetries were measured in 165 4-dimensional kinematic bins, covering the widest kinematic range ever explored simultaneously for beam and target-polarization observables in the valence quark region. The kinematic dependences of the obtained asymmetries are discussed and compared to the predictions of models of Generalized Parton Distributions. The measurement of three DVCS spin observables at the same kinematic points allows a quasi-model-independent extraction of the imaginary parts of the $H$ and $\tilde{H}$ Compton Form Factors, which give insight into the electric and axial charge distributions of valence quarks in the proton.

Towards one-loop SYM amplitudes from the pure spinor BRST cohomology

In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to type IIA/B supergravity amplitudes as a byproduct. At six points, the sources of the hexagon anomaly are identified in superspace as systematic obstructions to BRST invariance. Our results are expected to reproduce any integrated SYM amplitude in dimensions .

Double Parton Scattering at High Energies

We discuss a few examples of rich newly developing field of double parton scattering. We start our presentation from production of two pairs of charm quark-antiquark and argue that it is the golden reaction to study the double parton scattering effects. In addition to the DPS we consider briefly also mechanism of single parton scattering and show that it gives much smaller contribution to the $c \bar c c \bar c$ final state. Next we discuss a perturbative parton-splitting mechanism which should be included in addition to the conventional DPS mechanism. We show that the presence of this mechanism unavoidably leads to collision energy and other kinematical variables dependence of so-called $\sigma_{eff}$ parameter being extracted from different experiments. Next we briefly discuss production of four jets. We concentrate on estimation of the contribution of DPS for jets remote in rapidity. Understanding of this contribution is very important in the context of searches for BFKL effects known under the the name Mueller-Navelet jets. We discuss the situation in a more general context. Finally we briefly mention about DPS effects in production of $W^+ W^-$. Outlook closes the presentation.

Spin density matrix elements in exclusive $$\omega $$ ω electroproduction on $$^1$$ 1 H and $$^2$$ 2 H targets at 27.5 GeV beam energy

Spin Density Matrix Elements (SDMEs) describing the angular distribution of exclusive ρ 0 electroproduction and decay are determined in the HERMES experiment with 27.6 GeV beam energy and unpolarized hydrogen and deuterium targets. Eight (fifteen) SDMEs that are related (unrelated) to the longitudinal polarization of the beam are extracted in the kinematic region 1<Q 2<7 GeV2, 3.0<W<6.3 GeV, and −t<0.4 GeV2. Within the given experimental uncertainties, a hierarchy of relative sizes of helicity amplitudes is observed. Kinematic dependences of all SDMEs on Q 2 and t are presented, as well as the longitudinal-to-transverse ρ 0 electroproduction cross-section ratio as a function of Q 2. A small but statistically significant deviation from the hypothesis of s-channel helicity conservation is observed. An indication is seen of a contribution of unnatural-parity-exchange amplitudes; these amplitudes are naturally generated with a quark-exchange mechanism.

KINEMATIC MODELING OF THE MILKY WAY USING THE RAVE AND GCS STELLAR SURVEYS

We investigate the kinematic parameters of the Milky Way disc using the RAVE and GCS stellar surveys. We do this by fitting a kinematic model to the data taking the selection function of the data into account. For stars in the GCS we use all phase-space coordinates, but for RAVE stars we use only $(l,b,v_{\rm los})$. Using MCMC technique, we investigate the full posterior distributions of the parameters given the data. We investigate the `age-velocity dispersion' relation for the three kinematic components ($\sigma_R,\sigma_{\phi},\sigma_z$), the radial dependence of the velocity dispersions, the Solar peculiar motion ($U_{\odot},V_{\odot}, W_{\odot} $), the circular speed $\Theta_0$ at the Sun and the fall of mean azimuthal motion with height above the mid-plane. We confirm that the Besan\c{c}on-style Gaussian model accurately fits the GCS data, but fails to match the details of the more spatially extended RAVE survey. In particular, the Shu distribution function (DF) handles non-circular orbits more accurately and provides a better fit to the kinematic data. The Gaussian distribution function not only fits the data poorly but systematically underestimates the fall of velocity dispersion with radius. We find that correlations exist between a number of parameters, which highlights the importance of doing joint fits. The large size of the RAVE survey, allows us to get precise values for most parameters. However, large systematic uncertainties remain, especially in $V_{\odot}$ and $\Theta_0$. We find that, for an extended sample of stars, $\Theta_0$ is underestimated by as much as $10\%$ if the vertical dependence of the mean azimuthal motion is neglected. Using a simple model for vertical dependence of kinematics, we find that it is possible to match the Sgr A* proper motion without any need for $V_{\odot}$ being larger than that estimated locally by surveys like GCS.

Study of the kinematic dependences of Λ b 0 production in pp collisions and a measurement of the Λ b 0 → Λ c + π − branching fraction

The kinematic dependences of the relative production rates, $f_{\Lambda_b^0}/f_d$, of $\Lambda_b^0$ baryons and $\bar{B}^0$ mesons are measured using $\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^-$ and $\bar{B}^0 \rightarrow D^+ \pi^-$ decays. The measurements use proton-proton collision data, corresponding to an integrated luminosity of 1 fb$^{-1}$ at a centre-of-mass energy of 7 TeV, recorded in the forward region with the LHCb experiment. The relative production rates are observed to depend on the transverse momentum, $p_T$, and pseudorapidity, $\eta$, of the beauty hadron, in the studied kinematic region $1.5 < p_T < 40$ GeV/$c$ and $2 < \eta < 5$. Using a previous LHCb measurement of $f_{\Lambda_b^0}/f_d$ in semileptonic decays, the branching fraction $\mathcal{B}(\Lambda_b^0 \rightarrow \Lambda_c^+ \pi^-) = \Big( 4.30 \pm 0.03 \,\, ^{+0.12}_{-0.11} \pm 0.26 \pm 0.21 \Big) \times 10^{-3}$ is obtained, where the first uncertainty is statistical, the second is systematic, the third is from the previous LHCb measurement of $f_{\Lambda_b^0}/f_d$ and the fourth is due to the $\bar{B}^0 \rightarrow D^+ \pi^-$ branching fraction. This is the most precise measurement of a $\Lambda_b^0$ branching fraction to date.

Spin alignment and violation of the OZI rule in exclusive ω and ϕ production in pp collisions

Exclusive production of the isoscalar vector mesons ω and ϕ is measured with a 190 GeV/c proton beam impinging on a liquid hydrogen target. Cross section ratios are determined in three intervals of the Feynman variable xF of the fast proton. A significant violation of the OZI rule is found, confirming earlier findings. Its kinematic dependence on xF and on the invariant mass MpV of the system formed by fast proton pfast and vector meson V is discussed in terms of diffractive production of pfastV resonances in competition with central production. The measurement of the spin density matrix element ρ00 of the vector mesons in different selected reference frames provides another handle to distinguish the contributions of these two major reaction types. Again, dependences of the alignment on xF and on MpV are found. Most of the observations can be traced back to the existence of several excited baryon states contributing to ω production which are absent in the case of the ϕ meson. Removing the low-mass MpV resonant region, the OZI rule is found to be violated by a factor of eight, independently of xF.

Measurement of azimuthal hadron asymmetries in semi-inclusive deep inelastic scattering off unpolarised nucleons

Spin-averaged asymmetries in the azimuthal distributions of positive and negative hadrons produced in deep inelastic scattering were measured using the CERN SPS longitudinally polarised muon beam at 160 GeV/c and a 6LiD target. The amplitudes of the three azimuthal modulations cos⁡ϕh, cos⁡2ϕh and sin⁡ϕh were obtained binning the data separately in each of the relevant kinematic variables x, z or pTh and binning in a three-dimensional grid of these three variables. The amplitudes of the cos⁡ϕh and cos⁡2ϕh modulations show strong kinematic dependencies both for positive and negative hadrons.

Определение кинематических зависимостей глухого пиления круглыми пилами

Определение кинематических зависимостей глухого пиления круглыми пилами

On hyperlogarithms and Feynman integrals with divergences and many scales

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples of integrations of three- and four-point integrals in Schwinger parameters with non-trivial kinematic dependence, involving setups with off-shell external momenta and differently massive internal propagators. The full set of Feynman graphs admissible to parametric integration is not yet understood and we discuss some counterexamples to the crucial property of linear reducibility. Furthermore we clarify how divergent integrals can be approached in dimensional regularization with this algorithm.